sinxcosx = 1/3
(sinx + cosx)^2 = 1+2sinxcosx = 5/3
因为
0≤x≤π/2
所以
sinx + cosx > 0
所以
sinx + cosx = (根号15) / 3
所以
1/(1+sinx) + 1/(1+cosx)
= (2+sinx+cosx)/((1+sinx)(1+cosx))
= (2+sinx+cosx)/(1+sinx+cosx+sinxcosx)
= (2 + (根号15) / 3) / (1 + (根号15) / 3 + 1/3)
= (6 + 根号15) / (4 + 根号15)
= (6 + 根号15)(4 - 根号15)
= 9 - 2根号15